As someone who frequently r/theydidthemaths, r/theydidthemonstermaths, and r/genshinmemepact on Reddit, this has got to be the best mix of all three. The video was great fun!
Fun fact: If Faruzan's enhanced charged attack hits the ground it activates on the ground But if it hits an enemy, it activates on the enemy Likewise, if it hits a player, it activates on the player and deletes the arrow This is the only instance I know of in Genshin where aiming at another player actually blocks your attack, other than the ball octopus power up in Fontaine Also it doesn't do the same with that girl whose name escapes me, but something about A Statue of Her Excellency, the Almighty Narukami Ogosho, God of Thunder
Thanks for the complement :) Yeah it feels like resinless behavior but I honestly have a lot of stuff I still need to do besides resin related activities (exploration, world quests, character story quests, archon quests). Heck, I still haven't done Venti's Story Quest and I've been playing since 1.0 lol.
@@CountSacke Venti's Story Quest IS *GOLD*, I SWEAR But I feel you with the procrastination X"DDD I've gotten max completion before, and then I had a few years gap in playing, and now I'm the master procrastinator when it comes to Character Story Quests as well o7 :I X"DD
Would like to mention that I actually don't know if arrows have a terminal velocity so that's another thing that can be added into the recommendations lol
I thought this was going to be just a boring video about genshin I could sleep to but then my guy started used cinematic formulas and I got immediately hooked to the screen 😂
Hello Cont Sacke! I didn't expect that you actually conducted experiments and carried out simulations even 400 times to estimate the parameters. Thank you also for your efforts and hard work. Also know that I am one of the people who supports you in creating content, so don't be discouraged from creating unique content like this. Come on RUclips!😡
Thank you so much for your words of encouragement, it's great to know that you enjoyed the video as the one who suggested the topic in the first place :) Also, I honestly thought you had forgotten about me. Seeing that you're the first to comment surprised me and it's nice to know that you were still around waiting for my upload, thank you for your patience. I don't really blame RUclips that much for videos that underperform. Every video creator on the platform has to compete with it after all. Btw, the 400 samples I mentioned are for the actual measurements I did for the results of vi and Rarm. The simulations were done separately, though it's relatively easy to increase the simulated samples once you've implemented them. If I included the simulated samples, then the sample count would probably actually go into the thousands.
This is high quality content, even if you are just seeing this out of curiousity, its easy to understand!! Im happy youtube recommended me this channel, how you grow fast, i was surprised to onli see 1k subs on a channel with this quality!
I had this video playing in the background while doing my calculus homework. Don't take this the wrong way, but I love playing videos like this and only paying attention to them for like two seconds when I start to zone out from my work. Hearing someone speaking the kinds of thoughts that are supposed to be going through my head helps me refocus. I also love your music choices. It probably wasn't your goal to make this kind of experience when you made this video, but it made my day better nonetheless!
Hi, I'm glad that the video was able to help you focus. Don't worry, I understand that not everyone puts 100% of their attention while watching videos, I mean I'm pretty sure everyone does that to some extent regardless of the type of videos they watch. Also, thank you for your compliments about the music choices. I love Genshin's music a lot and I always try to look for underrated songs while also arranging them in a more seamless manner.
holy moly it’s finally here!! ❤❤❤ i love this video sm! I wish i had the vocabulary to express my genuine appreciation for your videos. All i can think of is “wow this is so cool!”, which isn’t even close to enough
I already love your content, even though i didn't understood a single thing from this video 😅. You've put a massive amount of work into this and i'm here for it! Wish you luck! ❤
Impressive video! The experiment methodology, in particular, was highly ingenious. One thing you seem to have forgotten, however, is model validation. You have not quite established that the arrows in-game do indeed follow the model (based on real-world physics) that you have derived. Indeed, you imply as much when you mention that you don't know if arrows have a terminal velocity. While it can be inferred from the data that arrows move at constant speed for the first t_a time, it cannot be similarly inferred without more extensive analysis that the gravitational pull is constant over time after t_a. Furthermore, the idea that arrows are fired from the end of your arm is not at all supported by data, with R_a even being negative. Instead, it seems just as likely (if not more from a game programming perspective) that the arrow is fired from your character's coordinate position. This difference would not at all be noticeable by the naked eye.
Hello, thank you for your compliments and for your insightful critique. I have mentioned under my recommendations in the last part of the video that I or someone else needs to come up with an experiment to validate my model in the first place. I have an idea for how to do this but this video was getting very long so I thought it would be best saved for a part 2. In regards to the constant acceleration, yes that is something that I would have to validate as stated in my previous paragraph. Most of the time in game programming, kinematics is all that's really used so I assumed that would be the case. If the evidence says otherwise, then of course I'll have to fix that. Lastly about R_arm, it is very possible that is the case. Someone else in the comments, @pr0ntab, actually mentioned it to me that they hypothesize that R_arm = 0 while also explaining why in terms of game development programming. It was quite convincing. I initially added it to the model just because of how that would actually work irl, but it is very likely that what you say is true. Though that assumes that you're measuring time from the first frame that you see the character begins the animation for firing the arrow, which from what I recall, the arrow isn't visible on that frame.
Damn you Mihoyo for all these complicated maths in a gatcha game! Mihoyo: Fuu-fuu-fuu... All according to keikaku. We are improving the maths skillz of the player base.
Lol. It's actually quite reasonable as to why this math is found in the game. Kinematics is one of the most essential topics to understand in game programming. It's literally the physics of movement so it's quite natural for it to pop up in a game that let's the player move. What's nice is that Hoyo gave enough information to let this be possible :)
20:57 The equation can be simplified to β⃗̂=χ⁻¹y⃗ β⃗̂=(χᵀχ)⁻¹χᵀy⃗ β⃗̂=χ⁻¹(χᵀ)⁻¹χᵀy⃗ β⃗̂=χ⁻¹y⃗ That being said, I guess calulating (χᵀχ)⁻¹ is easier than χ⁻¹ 24:22 The equation on screen is wrong, but the narration is correct.
About X^-1, X is generally not a square matrix so you can't really take the inverse of it. It has dimensions of (n, p) where n is the number of samples and p is the number of beta parameters used. And lol yeah, I did spend a lot of time re-watching my footage to make sure there were no errors. If I'm not mistaken I've rendered this video 3 times due to mistakes, but with a video as long as this one, a few are bound to slip through. Whoops
I'm not really sure what the pseudo-inverse/Moore-Penrose matrix is so I can't really say if you're right or not, but if anything, the equation for the estimators of beta are derived using the method of least squares.
When taking measurements during the experiment phase, were you able to consider possible error margins caused by graphics settings? Or were these values measured at maximum graphics settings? (Very cool video btw, you earned a new subscriber!)
Hello, thanks for subscribing! I very much appreciate the support :) I don't believe any of the measurements I've done in this particular video are influenced by the graphics settings. As far as I know, graphics settings only matter when considering pixel measurements which I didn't really do in this video. Most of the error is mainly in measuring time which can be influenced by lag. I did consider error margins with a 95% confidence interval shown in the results and analysis section for vi and Rarm.
Now that I've mentioned it, higher graphics settings can cause more lag so it is kinda influenced by it, but it's not really that much of an influence. I think as long as you're not experiencing frequent lag spikes, more samples should be able to account for this.
Yeah, this is one of those little things, that make the game's world amazing. Most other game's open world is just a 3D menu skin to navigate between the game's activities (and that is the reason these games make the world's traversal speed their top priority). I'm so glad Genshin is not among them, although kids these days, with their freakin mobile experience, do tend to view it like that.
I agree with you about how amazing Genshin's world is, but does this relate to the video? It's fine if you're just expressing a thought, I'm just curious. I'm not calling you out for commenting something unrelated if it is. I don't mind. I just want to make sure I'm understanding what your saying.
@@CountSacke yeah, sorry about that, just expressing a thought, after being thoroughly disappointed in WuWa. I was hoping for "Genshin 2.0" so to speak, and what I got is... underwhelming. And now the new hope, Neverness to Everness, seems to fall to the same path. I want to believe I'm wrong, but what I see is rather alarming. Kids don't seem to understand what the problem is, since for mobile players, the vast open world is rather nuisance.
Sorry, I'm a little confused, what do you think the problem is? You mentioned that some games feel like a "3D menu skin" but I'm not sure I understand what that means.
@@CountSacke I think the problem is overly sterilized environment. Like for example, in Wuthering Waves: you can't burn grass, can't get wet standing in the water or in the rain. You need specific item to burn vines, your fire abilities will not work on them, contrary to your expectations. All enemy drops are not "in-game objects which are dropped", they are added directly into your inventory, you don't even see them falling down. And of course, there is no ballistics: all shots travel in a straight line, and then just vanish in the air. In Neverness to Everness (at least by now) it is even more noticeable: you can't fight in the open world at all, there is no enemies. Instead, you have to find specific spot and interact with it, which will teleport you into enclosed space with enemies. What is good about the open world like this, except the scenery? I feel like newer games become more and more primitive in regards to open world, and that is not what I want them to be.
From what I understand, what you're saying is that there seems to be a lack of connection between the game world's environment and the things that are happening around it? Based on what you're saying, it sounds like the immersion of the game's seems to be lacking. The little things that typically no one would see only until they're not there so to speak. Did I get that right?
Lol. I mean yeah I suppose I do always have a spreadsheet open to track my primogems so that I can properly budget for new characters. Though, as I've mentioned in another comment, there's still a lot of stuff I have yet to do that isn't resin related. On top of that, I just enjoy doing this thing to help get a better understanding of topics. I probably would have done this stuff regardless of if Genshin didn't have resin to begin with. I calculated physics in Geometry Dash about 5 years ago and that game practically has endless levels to play.
@CountSacke actually who doesn't though, this game's good enough to make us do things that other games don't And if we're not doing these kinds of things we're watching videos like yours about it XD
How to measure distance Map markers Yes its not perfect and hight isnt considered unless you use a already existing marker Edit: Start at an already existing marker on a rather flat field Shoot in the distance Have someone stand where you hit Have them match your shoot back to your position Measure distance Repeat
Interesting methodology, though, I'm not sure how you plan on "measuring the distance" on the final step in the first place. I have a few ways to measure distances but over the long distances that charged shots can fly, they may not be the most practical. In addition, I don't really have another person/alt account so I can't really do it ; - ; Also, I'm kinda wondering, why are you suggesting a distance measurement methdology? I just want make sure I know where you're coming from.
To the person who gaged at my Ganyu's Charged Shot Damage being only 9k and asking if she even had artifacts, yes she has artifacts. I don't know why I can't find your comment and I don't have any comments held for review at the moment so I can only assume that you chose to delete it. I found your comment in my gmail so I can confirm it did exist at some point (Yes, RUclips sends emails to you about comments left on videos). I purposely keep my characters slightly underpowered for a bit of a challenge. In summary this is where I've capped myself at the moment: character and weapon level at a maximum of 70 This also means that maximum talent levels are 6. Character Artifacts max enhancement 16 (most are still at 15 since I only recently decided to upgrade to 16) I hope that explains why my damage feels low for you.
HAHAHA to say I've underestimated this video's performance is definitely an understatement. It was only like a few hours ago that it suddenly blew up. Before (that which was about a day after it was uploaded), the video was at about 60 which was more than I expected but still reasonable. Also, glad you're here to stay :)
R_arm being negative or 0 makes sense if you imagine that arrows are spawned at that camera "pivot" (around which your aim swings when you move the mouse or joystick in aiming mode) and camera itself is positioned just behind that with the reticle centered. The arrow animation might be started slightly behind that point so you can arrow notch and travel on systems with high Fps. I don't think this is an error although my suspicion is that R_arm is just 0 and there might be some global measurement innacuracy when counting frames.
Hello! Interesting thoughts. Rarm being negative means that the arrow would start behind the player (based on how I've defined it) that's why I thought it didn't really make sense. If it were negative, you could have the player's back against the wall aiming away from it but the arrow would hit the wall behind them. I'm pretty sure that doesn't happen so that rules out the possibility of it being negative. As you mentioned, the reason my measurements were negative is likely just due to time measurement inaccuracies. As to if it could be zero, it's possible (it's within the 95% confidence intervals if anything), but it's hard to say with how large the standard error of Rarm is. The number could just be really close to zero (like maybe even 0.1 or smaller). I do think the initial position does depend on the vertical angle to some extent. To suggest that it's 0 means that it doesn't matter how how high the player aims, the arrow's initial position would always start from the center of the circular arc. That idea to me just doesn't sound right because I'm pretty sure the arrow's initial height is higher when aiming more upwards (though this could just be me idk). For now, I just hope someone can figure out another way to experimentally determine Rarm...
@CountSacke I think the best thing to do (and I'm gonna try this myself) is to look at how arrows are spawned in coop because that's going to be the most accurate version of what's really happening vs what you see in first-person.
@@CountSacke I bring all this up because I think Genshin does something similar to what shooter games do and it messes with collision and your ability to clip your model into geometry and does some visual hacks like hide the arrow when it's first fired in 3rd person so it doesn't look like it's clipped into your torso to make the aim mode experience make more sense. It's just a gut feeling based on your observations and it reminds me of the struggles fps game devs have with like rendering your hands/gun and where bullets emit from your model vs your reticle
Ah I think I misunderstood you. Your first comment sounds like someone has already measured the distance an arrow travels. What I believe you actually meant is that, based on the model I derived, the maximum distance should be 505 m. There are various ways to verify the equations (the one you mentioned is one of them). The main problem with this method assumes that you have an accurate way to make the player shoot at a 45° angle. Measuring angles accurately is one of the things that makes this very difficult on top of the distance being very large in the first place.
@@CountSacke Well, I tried and the actual in-game distance I got is closer to 400m. I had a daily quest at the shore near the Statue of The Seven at Ameyalco Waters, and was shooting from the small peninsula to the northeast. Both points are at sea level, floating islands serve as a good reference point, and from the island to the south-east of the target the whole trajectory can be observed. I tried a bunch of different angles, but the furthest I could reach was the center of the arena with the turtle, which was 104m from the quest location. Optimal angle is actually ~43.9°, because the trajectory have this straight segment, but near the optimal angle aiming error of 1° result in distance error of ~0.3m, so super accurate aim is not that important. To get 400m with given formula one need to aim at either 22° or 64°.
I see. There could be many reasons as to why there's a discrepancy between my model and the in-game results. Maybe the model is even just wrong after t_a seconds. However to determine the cause and narrow things down, I would need a lot more data than just one point. Just something I want to emphasize, the 0.3 m assumes that you can aim within ±1° of the correct angle (I doubt I can really aim with that level of accuracy). But yes, compared to the large distance arrows travel, 0.3 m error is practically negligible. Eliminating error when possible just makes sure that the parameters measured are more accurate so forgive me if I'm being strict about it.
Most likely projectile motion should be involved if the shots aren't in a completely straight line, but I'm not familiar War Thunder so I can't really say.
Lol yeah, but I remember spending like more than 10 minutes just trying to shoot a Falcon for the achievement before I had Yoimiya. I just wanted to recreate that feeling for the intro
Hmmm... could the R arm be negative bc it calculated starting from the hand up to the shoulder? I need to look at the full equation to determine this hypothesis 😅
Based on how I've defined R arm, the arrow should start at the tip of the bow. If you consider a circle with it's center at the player's chest, R arm should be the arm length of the character roughly speaking. The equation for measuring R arm is just for finding the best possible y-intercept of a line to the data.
Do you mean that my measurement of the arrow velocity seems is inaccurate or are you just expressing your thoughts about the arrows moving at 50 m/s feels slow?
@CountSacke just expressing my thoughts about the game. I did archery and it just looks wrong to me when I see the arrow move. I'm expecting it to hit much sooner because I'm used to arrows moving closer to 60 m/s.
![[5.1] The Most Important Symbol In Genshin.... Maybe - A Genshin Impact Theory](http://i.ytimg.com/vi/oFYIpNeY6Oc/mqdefault.jpg)
As someone who frequently r/theydidthemaths, r/theydidthemonstermaths, and r/genshinmemepact on Reddit, this has got to be the best mix of all three. The video was great fun!
ooh smelly🤤
Thank you :)
@@parryhotter8788you must be fun at parties
This video has made me a bowshot god. Birds in teyvat now fear me.
HAHAHA
Fun fact:
If Faruzan's enhanced charged attack hits the ground it activates on the ground
But if it hits an enemy, it activates on the enemy
Likewise, if it hits a player, it activates on the player and deletes the arrow
This is the only instance I know of in Genshin where aiming at another player actually blocks your attack, other than the ball octopus power up in Fontaine
Also it doesn't do the same with that girl whose name escapes me, but something about A Statue of Her Excellency, the Almighty Narukami Ogosho, God of Thunder
Did you mean, Kujou Sara for the last one?
Resinless behavoir ngl. But still this is a reslly high qualitiy vid. Thank you!
Thanks for the complement :)
Yeah it feels like resinless behavior but I honestly have a lot of stuff I still need to do besides resin related activities (exploration, world quests, character story quests, archon quests). Heck, I still haven't done Venti's Story Quest and I've been playing since 1.0 lol.
Lmao
@@CountSackebro the quest procrastination is so realllll
@ekthepro HAHAHA yeah.
@@CountSacke Venti's Story Quest IS *GOLD*, I SWEAR
But I feel you with the procrastination X"DDD I've gotten max completion before, and then I had a few years gap in playing, and now I'm the master procrastinator when it comes to Character Story Quests as well o7 :I
X"DD
This is the first time i see your video. RUclips algorithm brought me here and in fucking happy
I'm glad to hear that you enjoyed :)
I came to Genshin after years of playing War Thunder. All the time shooting down planes with tank guns really helped.
I see. Interesting
Would like to mention that I actually don't know if arrows have a terminal velocity so that's another thing that can be added into the recommendations lol
I understood projectile motion here better that in class
Glad that it helped you :)
Dad: Son are you SIMPING?
Me: No just PHYSICS
HAHAHA Why not both?
Omg tomorrow I am writing test from classical mechanics, this helped me a lot, thanks!
Glad it helped you review :)
Good luck on your test!
@@CountSacke I just finished. 15 out of 12 points :D
@@antihmota4625 Congratulations! :)
I thought this was going to be just a boring video about genshin I could sleep to but then my guy started used cinematic formulas and I got immediately hooked to the screen 😂
Hahaha. Glad that you found it interesting :)
And I suppose the kinematic equations are quite cinematic.
@CountSacke lol sorry, in spanish kinematics are called cinematics my bad😔🤣
Ah I see, it's okay. haha
I can't help but click on a good physics video, I love learning so much but teachers make it to torturous 😭
Thank you for the compliment :)
Hopefully you were able to understand what I was explaining in the video.
omg i remember i wondered about this when i started playing, never expected someone to actually calculate it and post it
Haha. It was only a matter of time until someone started doing Genshin Physics.
Hello Cont Sacke!
I didn't expect that you actually conducted experiments and carried out simulations even 400 times to estimate the parameters. Thank you also for your efforts and hard work. Also know that I am one of the people who supports you in creating content, so don't be discouraged from creating unique content like this. Come on RUclips!😡
Thank you so much for your words of encouragement, it's great to know that you enjoyed the video as the one who suggested the topic in the first place :)
Also, I honestly thought you had forgotten about me. Seeing that you're the first to comment surprised me and it's nice to know that you were still around waiting for my upload, thank you for your patience.
I don't really blame RUclips that much for videos that underperform. Every video creator on the platform has to compete with it after all.
Btw, the 400 samples I mentioned are for the actual measurements I did for the results of vi and Rarm. The simulations were done separately, though it's relatively easy to increase the simulated samples once you've implemented them. If I included the simulated samples, then the sample count would probably actually go into the thousands.
This is high quality content, even if you are just seeing this out of curiousity, its easy to understand!!
Im happy youtube recommended me this channel, how you grow fast, i was surprised to onli see 1k subs on a channel with this quality!
Thank you soo much for your kind words :)
I'm glad that you were able to understand the video.
dude how do you only have 1.7k views, this is an incredible video, keep it up
Tysm :) It makes me really happy to hear that you enjoyed it.
I had this video playing in the background while doing my calculus homework. Don't take this the wrong way, but I love playing videos like this and only paying attention to them for like two seconds when I start to zone out from my work. Hearing someone speaking the kinds of thoughts that are supposed to be going through my head helps me refocus. I also love your music choices. It probably wasn't your goal to make this kind of experience when you made this video, but it made my day better nonetheless!
It also just occured to me that Ororon (tall male archer) should be in the next banner, and is a little easier to get, as he is a four-star
Hi, I'm glad that the video was able to help you focus. Don't worry, I understand that not everyone puts 100% of their attention while watching videos, I mean I'm pretty sure everyone does that to some extent regardless of the type of videos they watch.
Also, thank you for your compliments about the music choices. I love Genshin's music a lot and I always try to look for underrated songs while also arranging them in a more seamless manner.
Oh, about Ororon, I don't think I'll be pulling on any of the banners for next patch so it's a bit unfortunate.
holy moly it’s finally here!! ❤❤❤ i love this video sm! I wish i had the vocabulary to express my genuine appreciation for your videos. All i can think of is “wow this is so cool!”, which isn’t even close to enough
Thank you so much :)
It's nice to know you still remember me
I got physics exam in two weeks... and i love genshin... THIS IS PERFECT 😍
Good luck on your exam! :)
I already love your content, even though i didn't understood a single thing from this video 😅. You've put a massive amount of work into this and i'm here for it! Wish you luck! ❤
Ty :)
Sorry that you weren't able to understand it though. If you want I could clarify some things.
Commenting for the algorithm, good luck with your content creation journey
Thank you :)
Impressive video! The experiment methodology, in particular, was highly ingenious. One thing you seem to have forgotten, however, is model validation. You have not quite established that the arrows in-game do indeed follow the model (based on real-world physics) that you have derived. Indeed, you imply as much when you mention that you don't know if arrows have a terminal velocity.
While it can be inferred from the data that arrows move at constant speed for the first t_a time, it cannot be similarly inferred without more extensive analysis that the gravitational pull is constant over time after t_a. Furthermore, the idea that arrows are fired from the end of your arm is not at all supported by data, with R_a even being negative. Instead, it seems just as likely (if not more from a game programming perspective) that the arrow is fired from your character's coordinate position. This difference would not at all be noticeable by the naked eye.
Hello, thank you for your compliments and for your insightful critique.
I have mentioned under my recommendations in the last part of the video that I or someone else needs to come up with an experiment to validate my model in the first place. I have an idea for how to do this but this video was getting very long so I thought it would be best saved for a part 2.
In regards to the constant acceleration, yes that is something that I would have to validate as stated in my previous paragraph. Most of the time in game programming, kinematics is all that's really used so I assumed that would be the case. If the evidence says otherwise, then of course I'll have to fix that.
Lastly about R_arm, it is very possible that is the case. Someone else in the comments, @pr0ntab, actually mentioned it to me that they hypothesize that R_arm = 0 while also explaining why in terms of game development programming. It was quite convincing. I initially added it to the model just because of how that would actually work irl, but it is very likely that what you say is true. Though that assumes that you're measuring time from the first frame that you see the character begins the animation for firing the arrow, which from what I recall, the arrow isn't visible on that frame.
@@CountSacke Thanks for the very detailed answer! Looking forward to part 2!
was very interesting to listen to!
lol Thank you :)
Banger video ngl
Thanks :)
I really enjoyed this. Thank you!
Glad you liked it :)
Finally out of my watch later of thousands of videos, haya
Haha, well considering how recent this video was uploaded, I think you did a good job.
Damn you Mihoyo for all these complicated maths in a gatcha game!
Mihoyo: Fuu-fuu-fuu... All according to keikaku. We are improving the maths skillz of the player base.
Lol. It's actually quite reasonable as to why this math is found in the game.
Kinematics is one of the most essential topics to understand in game programming. It's literally the physics of movement so it's quite natural for it to pop up in a game that let's the player move. What's nice is that Hoyo gave enough information to let this be possible :)
Omg I am a scientist and didn't think I would ever find a scientific study on genshin 😂
Haha, I do these things so I can also refine my understanding of various topics on top of just enjoying it in the first place
@ ❤️
20:57 The equation can be simplified to β⃗̂=χ⁻¹y⃗
β⃗̂=(χᵀχ)⁻¹χᵀy⃗
β⃗̂=χ⁻¹(χᵀ)⁻¹χᵀy⃗
β⃗̂=χ⁻¹y⃗
That being said, I guess calulating (χᵀχ)⁻¹ is easier than χ⁻¹
24:22 The equation on screen is wrong, but the narration is correct.
About X^-1, X is generally not a square matrix so you can't really take the inverse of it. It has dimensions of (n, p) where n is the number of samples and p is the number of beta parameters used.
And lol yeah, I did spend a lot of time re-watching my footage to make sure there were no errors. If I'm not mistaken I've rendered this video 3 times due to mistakes, but with a video as long as this one, a few are bound to slip through. Whoops
@CountSacke Ah, so (χᵀχ)⁻¹χᵀ is the pseudo-inverse (more specifically the Moore-Penrose)
I'm not really sure what the pseudo-inverse/Moore-Penrose matrix is so I can't really say if you're right or not, but if anything, the equation for the estimators of beta are derived using the method of least squares.
When taking measurements during the experiment phase, were you able to consider possible error margins caused by graphics settings? Or were these values measured at maximum graphics settings? (Very cool video btw, you earned a new subscriber!)
Hello, thanks for subscribing! I very much appreciate the support :)
I don't believe any of the measurements I've done in this particular video are influenced by the graphics settings. As far as I know, graphics settings only matter when considering pixel measurements which I didn't really do in this video.
Most of the error is mainly in measuring time which can be influenced by lag. I did consider error margins with a 95% confidence interval shown in the results and analysis section for vi and Rarm.
Now that I've mentioned it, higher graphics settings can cause more lag so it is kinda influenced by it, but it's not really that much of an influence. I think as long as you're not experiencing frequent lag spikes, more samples should be able to account for this.
Yeah, this is one of those little things, that make the game's world amazing. Most other game's open world is just a 3D menu skin to navigate between the game's activities (and that is the reason these games make the world's traversal speed their top priority). I'm so glad Genshin is not among them, although kids these days, with their freakin mobile experience, do tend to view it like that.
I agree with you about how amazing Genshin's world is, but does this relate to the video? It's fine if you're just expressing a thought, I'm just curious.
I'm not calling you out for commenting something unrelated if it is. I don't mind. I just want to make sure I'm understanding what your saying.
@@CountSacke yeah, sorry about that, just expressing a thought, after being thoroughly disappointed in WuWa. I was hoping for "Genshin 2.0" so to speak, and what I got is... underwhelming. And now the new hope, Neverness to Everness, seems to fall to the same path. I want to believe I'm wrong, but what I see is rather alarming. Kids don't seem to understand what the problem is, since for mobile players, the vast open world is rather nuisance.
Sorry, I'm a little confused, what do you think the problem is? You mentioned that some games feel like a "3D menu skin" but I'm not sure I understand what that means.
@@CountSacke I think the problem is overly sterilized environment. Like for example, in Wuthering Waves: you can't burn grass, can't get wet standing in the water or in the rain. You need specific item to burn vines, your fire abilities will not work on them, contrary to your expectations. All enemy drops are not "in-game objects which are dropped", they are added directly into your inventory, you don't even see them falling down. And of course, there is no ballistics: all shots travel in a straight line, and then just vanish in the air.
In Neverness to Everness (at least by now) it is even more noticeable: you can't fight in the open world at all, there is no enemies. Instead, you have to find specific spot and interact with it, which will teleport you into enclosed space with enemies. What is good about the open world like this, except the scenery? I feel like newer games become more and more primitive in regards to open world, and that is not what I want them to be.
From what I understand, what you're saying is that there seems to be a lack of connection between the game world's environment and the things that are happening around it?
Based on what you're saying, it sounds like the immersion of the game's seems to be lacking. The little things that typically no one would see only until they're not there so to speak.
Did I get that right?
Genshin player trying to not open excel while playing challenge (impossible):
The things we do when we are out of resin
Lol. I mean yeah I suppose I do always have a spreadsheet open to track my primogems so that I can properly budget for new characters.
Though, as I've mentioned in another comment, there's still a lot of stuff I have yet to do that isn't resin related. On top of that, I just enjoy doing this thing to help get a better understanding of topics. I probably would have done this stuff regardless of if Genshin didn't have resin to begin with. I calculated physics in Geometry Dash about 5 years ago and that game practically has endless levels to play.
@CountSacke actually who doesn't though, this game's good enough to make us do things that other games don't
And if we're not doing these kinds of things we're watching videos like yours about it XD
HAHAHA True
i will remember you
:) Tyty
40:25 that’s ok, there may or may not be a viable alternative coming up very soon 👀
Oh lol. I think I know who you're talking about but uhh, I also don't think I'm going to wish for that person RIP
How to measure distance
Map markers
Yes its not perfect and hight isnt considered unless you use a already existing marker
Edit:
Start at an already existing marker on a rather flat field
Shoot in the distance
Have someone stand where you hit
Have them match your shoot back to your position
Measure distance
Repeat
Interesting methodology, though, I'm not sure how you plan on "measuring the distance" on the final step in the first place. I have a few ways to measure distances but over the long distances that charged shots can fly, they may not be the most practical. In addition, I don't really have another person/alt account so I can't really do it ; - ;
Also, I'm kinda wondering, why are you suggesting a distance measurement methdology? I just want make sure I know where you're coming from.
@@CountSackeidk
I watched the video when I was rather tired, as I just woke up
Actually fell asleep and watched it twice ...
Might do it again 😂
HAHAHA As long as you're enjoying the video :)
To the person who gaged at my Ganyu's Charged Shot Damage being only 9k and asking if she even had artifacts, yes she has artifacts. I don't know why I can't find your comment and I don't have any comments held for review at the moment so I can only assume that you chose to delete it. I found your comment in my gmail so I can confirm it did exist at some point (Yes, RUclips sends emails to you about comments left on videos).
I purposely keep my characters slightly underpowered for a bit of a challenge. In summary this is where I've capped myself at the moment:
character and weapon level at a maximum of 70
This also means that maximum talent levels are 6.
Character Artifacts max enhancement 16 (most are still at 15 since I only recently decided to upgrade to 16)
I hope that explains why my damage feels low for you.
"30 to 50 views at most", would be a good prediction... for astronomy standards.
Missed some orders of magnitude there, mathboi. See you next vid
HAHAHA to say I've underestimated this video's performance is definitely an understatement. It was only like a few hours ago that it suddenly blew up. Before (that which was about a day after it was uploaded), the video was at about 60 which was more than I expected but still reasonable.
Also, glad you're here to stay :)
i like your funny words magic man
lol magic man?
R_arm being negative or 0 makes sense if you imagine that arrows are spawned at that camera "pivot" (around which your aim swings when you move the mouse or joystick in aiming mode) and camera itself is positioned just behind that with the reticle centered. The arrow animation might be started slightly behind that point so you can arrow notch and travel on systems with high Fps.
I don't think this is an error although my suspicion is that R_arm is just 0 and there might be some global measurement innacuracy when counting frames.
Hello! Interesting thoughts.
Rarm being negative means that the arrow would start behind the player (based on how I've defined it) that's why I thought it didn't really make sense. If it were negative, you could have the player's back against the wall aiming away from it but the arrow would hit the wall behind them. I'm pretty sure that doesn't happen so that rules out the possibility of it being negative. As you mentioned, the reason my measurements were negative is likely just due to time measurement inaccuracies.
As to if it could be zero, it's possible (it's within the 95% confidence intervals if anything), but it's hard to say with how large the standard error of Rarm is. The number could just be really close to zero (like maybe even 0.1 or smaller).
I do think the initial position does depend on the vertical angle to some extent. To suggest that it's 0 means that it doesn't matter how how high the player aims, the arrow's initial position would always start from the center of the circular arc. That idea to me just doesn't sound right because I'm pretty sure the arrow's initial height is higher when aiming more upwards (though this could just be me idk).
For now, I just hope someone can figure out another way to experimentally determine Rarm...
@CountSacke I think the best thing to do (and I'm gonna try this myself) is to look at how arrows are spawned in coop because that's going to be the most accurate version of what's really happening vs what you see in first-person.
Good idea. Let me know about your findings once you've tried it.
@@CountSacke I bring all this up because I think Genshin does something similar to what shooter games do and it messes with collision and your ability to clip your model into geometry and does some visual hacks like hide the arrow when it's first fired in 3rd person so it doesn't look like it's clipped into your torso to make the aim mode experience make more sense. It's just a gut feeling based on your observations and it reminds me of the struggles fps game devs have with like rendering your hands/gun and where bullets emit from your model vs your reticle
@@pr0ntab Interesting. I'll keep that in mind.
Im now a bowshot god!
Nice HAHAHA
If the equations are correct, the maximum shooting range should be about 505 meters on flat ground.
Interesting, I can check that. May I know where this number came from though?
@@CountSacke just pluged in the formula in the desmos. graph id: xakixv1e0e
Ah I think I misunderstood you. Your first comment sounds like someone has already measured the distance an arrow travels. What I believe you actually meant is that, based on the model I derived, the maximum distance should be 505 m.
There are various ways to verify the equations (the one you mentioned is one of them). The main problem with this method assumes that you have an accurate way to make the player shoot at a 45° angle. Measuring angles accurately is one of the things that makes this very difficult on top of the distance being very large in the first place.
@@CountSacke Well, I tried and the actual in-game distance I got is closer to 400m. I had a daily quest at the shore near the Statue of The Seven at Ameyalco Waters, and was shooting from the small peninsula to the northeast. Both points are at sea level, floating islands serve as a good reference point, and from the island to the south-east of the target the whole trajectory can be observed. I tried a bunch of different angles, but the furthest I could reach was the center of the arena with the turtle, which was 104m from the quest location.
Optimal angle is actually ~43.9°, because the trajectory have this straight segment, but near the optimal angle aiming error of 1° result in distance error of ~0.3m, so super accurate aim is not that important. To get 400m with given formula one need to aim at either 22° or 64°.
I see. There could be many reasons as to why there's a discrepancy between my model and the in-game results. Maybe the model is even just wrong after t_a seconds. However to determine the cause and narrow things down, I would need a lot more data than just one point.
Just something I want to emphasize, the 0.3 m assumes that you can aim within ±1° of the correct angle (I doubt I can really aim with that level of accuracy). But yes, compared to the large distance arrows travel, 0.3 m error is practically negligible. Eliminating error when possible just makes sure that the parameters measured are more accurate so forgive me if I'm being strict about it.
Now I'm curious if you can apply this logic to ammo ballistics in War Thunder in some way.
Most likely projectile motion should be involved if the shots aren't in a completely straight line, but I'm not familiar War Thunder so I can't really say.
Well even if they are in a perfectly straight line then it's still projectile motion technically lol. Just that g = 0.
solution: use yoimiya the aimbot😂
Lol yeah, but I remember spending like more than 10 minutes just trying to shoot a Falcon for the achievement before I had Yoimiya. I just wanted to recreate that feeling for the intro
@CountSacke 😂👍
We same
An hour video on Genshin Impact arrows? Like commented and subscribed 👍
Thank you so much, glad you liked it :)
Hmmm... could the R arm be negative bc it calculated starting from the hand up to the shoulder?
I need to look at the full equation to determine this hypothesis 😅
Based on how I've defined R arm, the arrow should start at the tip of the bow. If you consider a circle with it's center at the player's chest, R arm should be the arm length of the character roughly speaking.
The equation for measuring R arm is just for finding the best possible y-intercept of a line to the data.
I am not sure watching guideline on using bow characters or learning physics 😁
Haha, why not both? ¯\_(ツ)_/¯
What did you use to overlay the equations
Hello, the equations on screen were done in my video editor Da Vinci Resolve. Though, I use a digital painting software to write them.
the arrows move soooooooo slowly
Do you mean that my measurement of the arrow velocity seems is inaccurate or are you just expressing your thoughts about the arrows moving at 50 m/s feels slow?
@CountSacke just expressing my thoughts about the game. I did archery and it just looks wrong to me when I see the arrow move. I'm expecting it to hit much sooner because I'm used to arrows moving closer to 60 m/s.
Ah I see. Thanks for clarifying.
Nice
Ty ty :)
Skill isssue
Yes HAHAHA very much so
Use Yoimiya you'll get it I swear
Uhhhhhhhhh, what? Hahaha.
@CountSacke Yoimiya's charged attack has homing missiles
They're a bit faster than a falcon
AHHH, ok yeah.
Idk if this was intentional but you sound like the “how it’s made” guy
Lol really?
Why am I watching this…?
¯\_(ツ)_/¯
liked!
tyty :)
Is this video created on the Creator Experience Server?
If not why are there two unreleased characters in your team
No I play on the Asia server.
What's the Creator Experience Server and who are the two unreleased characters?
what are you studying in
I'm taking up Mechanical Engineering
Holy yapping 💀
Was it a bit too much? Haha
NERD
cool video tho fr
Haha thanks :)
What can I say, I'm going into engineering
Hi
Hello hello hello :)